- FindStat

Identifier

Mp00057: Parking functions —to touch composition⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤ

Values

[1,2,3,4] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[1,2,4,3] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[1,3,2,4] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[1,3,4,2] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[1,4,2,3] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[1,4,3,2] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[2,1,3,4] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[2,1,4,3] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[2,3,1,4] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[2,3,4,1] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[2,4,1,3] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[2,4,3,1] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[3,1,2,4] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[3,1,4,2] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[3,2,1,4] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[3,2,4,1] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[3,4,1,2] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[3,4,2,1] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[4,1,2,3] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[4,1,3,2] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[4,2,1,3] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[4,2,3,1] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[4,3,1,2] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[4,3,2,1] => [1,1,1,1] => [1,1,1,1] => [1,1,1] => 1

[1,1,3,3,5] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,1,3,5,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,1,5,3,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,3,1,3,5] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,3,1,5,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,3,3,1,5] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,3,3,5,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,3,5,1,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,3,5,3,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,5,1,3,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,5,3,1,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,5,3,3,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,1,1,3,5] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,1,1,5,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,1,3,1,5] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,1,3,5,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,1,5,1,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,1,5,3,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,3,1,1,5] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,3,1,5,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,3,5,1,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,5,1,1,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,5,1,3,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[3,5,3,1,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[5,1,1,3,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[5,1,3,1,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[5,1,3,3,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[5,3,1,1,3] => [2,2,1] => [2,2,1] => [2,1] => 1

[5,3,1,3,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[5,3,3,1,1] => [2,2,1] => [2,2,1] => [2,1] => 1

[1,1,3,4,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,1,4,3,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,1,4,4,3] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,3,1,4,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,3,4,1,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,3,4,4,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,4,1,3,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,4,1,4,3] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,4,3,1,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,4,3,4,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,4,4,1,3] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,4,4,3,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[3,1,1,4,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[3,1,4,1,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[3,1,4,4,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[3,4,1,1,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[3,4,1,4,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[3,4,4,1,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,1,1,3,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,1,1,4,3] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,1,3,1,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,1,3,4,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,1,4,1,3] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,1,4,3,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,3,1,1,4] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,3,1,4,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,3,4,1,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,4,1,1,3] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,4,1,3,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[4,4,3,1,1] => [2,1,2] => [2,2,1] => [2,1] => 1

[1,1,3,4,5] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,1,3,5,4] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,1,4,3,5] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,1,4,5,3] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,1,5,3,4] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,1,5,4,3] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,3,1,4,5] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,3,1,5,4] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,3,4,1,5] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,3,4,5,1] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,3,5,1,4] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,3,5,4,1] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,4,1,3,5] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,4,1,5,3] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,4,3,1,5] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,4,3,5,1] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

[1,4,5,1,3] => [2,1,1,1] => [2,1,1,1] => [1,1,1] => 1

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search for individual values

searching the database for the individual values of this statistic

Description

The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.

Map

to touch composition

Description

Sends a parking function to the composition of its labelled Dyck path.

Map

first row removal

Description

Removes the first entry of an integer partition

Map

to partition

Description

Sends a composition to the partition obtained by sorting the entries.